Check the new index contains the old index based on stat time instead of segNum

library/dash/src/main/java/com/google/android/exoplayer2/source/dash/DefaultDashChunkSource.java

@@ -686,6 +686,8 @@ public class DefaultDashChunkSource implements DashChunkSource {
             newPeriodDurationUs, newRepresentation, extractorWrapper, segmentNumShift, newIndex);
       }
 
+      long oldIndexFirstSegmentNum = oldIndex.getFirstSegmentNum();
+      long oldIndexStartTimeUs = oldIndex.getTimeUs(oldIndexFirstSegmentNum);
       long oldIndexLastSegmentNum = oldIndex.getFirstSegmentNum() + oldIndexSegmentCount - 1;
       long oldIndexEndTimeUs =
           oldIndex.getTimeUs(oldIndexLastSegmentNum)
@@ -700,8 +702,10 @@ public class DefaultDashChunkSource implements DashChunkSource {
         // There's a gap between the old index and the new one which means we've slipped behind the
         // live window and can't proceed.
         throw new BehindLiveWindowException();
-      } else if (oldIndex.getFirstSegmentNum() >= newIndexFirstSegmentNum) {
-        // The new index contains the old one, continue process the next segment
+      } else if (oldIndexStartTimeUs >= newIndexStartTimeUs) {
+        // The new index overlaps with (but does not have a start position contained within) the old
+        // index. This can only happen if extra segments have been added to the start of the index.
+        // Continue process the next segment as is.
       } else {
         // The new index overlaps with the old one.
         newSegmentNumShift +=